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Subset Hypotheses Testing and Instrument Exclusion in the Linear Iv Regression

journal contribution
posted on 2023-05-19, 08:48 authored by Doko Tchatoka, S
his paper explores the sensitivity of plug-in subset tests to instrument exclusion in structural models. Identification-robust statistics based on the plug-in principle have been developed for testing hypotheses specified on subsets of the structural parameters. However, their robustness to instrument exclusion has not been investigated. This paper proposes an analysis of the asymptotic distributions of the limited information maximum likelihood (LIML) estimator and plug-in statistics when potential instruments are omitted. Our results provide several new insights and extensions of earlier studies. We show that the exclusion of instruments can eliminate the first-stage, thus weakening identification and invalidating the plug-in subset inference. However, when instrument omission does not affect LIML consistency, it preserves the plug-in subset test validity, although LIML is no longer asymptotically efficient. Unlike the instrumental variable (IV) estimator, the LIML estimator of the identified linear combination of the nuisance parameter is not asymptotically a Gaussian mixture, even without instrument exclusion.

History

Publication title

Econometric Theory

Volume

31

Issue

6

Pagination

1192-1228

ISSN

0266-4666

Department/School

College Office - College of Business and Economics

Publisher

Cambridge Univ Press

Place of publication

40 West 20Th St, New York, USA, Ny, 10011-4211

Rights statement

Copyright 2014 Cambridge University Press

Repository Status

  • Restricted

Socio-economic Objectives

Other economic framework not elsewhere classified

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